HVDC System Based on Cockcroft-Walton Generator

HVDC system based on Cockcroft-Walton generator

J.F.A.P. Cunha, MSc Student, IST, S.P.F. Pinto, IST, J.F.A Silva, IST

Abstract—In this work, a study was carried out to design a by transferring charge from one capacitor to another in half- three-phase AC-DC boost converter based on Cockcroft-Walton, cycle and, on the other half, recharge the ﬁrst one without converting a three-phase voltage to voltage levels of a HVDC discharging the second one. Adding several stages under no- system. The Cockcroft-Walton converter is connected to the grid using a matrix converter, taking advantage of its ability to control load conditions [2]: the output frequency, as well as the ability to transform the three-phase AC voltages and currents into a single-phase voltage Vo = 2nE (1) and current. A closed-loop controller is designed to control the output voltage with an inner current loop, ensuring an unitary where n is the number of stages and Vo is the output voltage. power factor in the AC side. Using the simulation software However, when adding a load, that condition is no longer MATLAB/Simulink, the converter is tested to verify and validate veriﬁed due to discharge through the load and due to the the proposed converter, and the obtained results are discussed. capacitor’s impedance. Consequently, there is a voltage drop Index terms - Cockcroft-Walton converter, AC-DC converter, HVDC, Matrix converter, Voltage controller ∆Vo, and a ripple voltage in the DC output, δVo [3]. Some assumptions are made to the next analysis [4]:

I.INTRODUCTION • Q1 = nQn; • The diodes are ideal; Through the years, society has become more dependent on 1 • Time constant of the capacitor is much lower com- electric energy, and with the environment being an important RC paring to the input AC period; issue to the political agenda, there has been increased research for cleaner energy, through renewable energy sources, where where, Q1 is the charge of the capacitor C1, Qn the charge wind power is one of the most promising [1]. As most of at Cn and R represents the load. the best locations onshore for wind farms are taken, offshore The ﬂuctuation observed at the output voltage is: turbines presents a good alternative, as the average wind speed ∆Q 2∆Q n∆Q % δVo = + + ... + (2) is 20 higher revealing a better exploitation potential of the C C C wind resource. 2 4 n Usually, in land, the electric power transmission is in Assuming all the capacitors are identical and have the same alternating current, but due to the reactive power generated capacitance (C1 = C2 = Cn): in submarines cables, over long distances, it is crucial to use ∆Q δV = (1 + 2 + ... + n) (3) a High Voltage Direct Current (HVDC) system. Given future o C investments on offshore wind farms, this work is focused on Solving the arithmetic progression, and considering the a new topology to achieve voltage levels of a HVDC system approximation, ∆Q = I , where I is the output current and based on a matrix converter and the Cockcroft-Walton (CW) fs f the voltage source frequency: voltage multiplier. s The necessary steps to achieve that are the following: I n(n + 1) δVo = (4) • Study the operation of Cockcroft-Walton converter; fsC 2 • Study the operation of matrix converter; Considering that any charge delivered to the load must ﬁrst • Study the principle of operation and design of the pro- work it’s way up the diode ladder, the voltage drop can be posed converter; obtained as: • Study and design the control system of CW converter output voltage, from current control; I 2n3 n ∆V = ( + ) (5) • o Simulate the proposed converter using MAT- fsC 3 3 LAB/Simulink software; III.COCKCROFT-WALTON WITH A MATRIX CONVERTER II.COCKCROFT-WALTON VOLTAGE MULTIPLIER Since a wind turbine generates a three-phase voltage, and Half Wave Cockcroft-Walton voltage multiplier is widely the CW is fed by a single-phase, this work proposes using a used among high-voltage dc applications. Converting AC volt- matrix converter, making it possible not only to transform a age in DC voltage, as shown in Fig. 1, it’s a cascade of diodes three-phase source to a single-phase source, but also control and capacitors containing two diodes and two capacitors in the matrix converter output frequency. As shown in Fig. 2, each stage. Theoretically, for only one stage, an AC voltage adding three boost inductors, it’s possible to have a higher with an amplitude of E, has an output of 2E DC voltage voltage gain than a conventional CW converter. VC1 VC(2n−1) A − + B ... − + (2γA − γB − γC )Vγ VAN = ... Vin D1 D2 D(2n−1) D2n 3 (2γB − γC − γA)Vγ C ... VBN = (7) − + − + 3 R G VC2 VC2n (2γ − γ − γ )V − + C A B γ Vo V = CN 3 Fig. 1: Half-Wave Cockcroft-Walton Voltage Multiplier.

iγ = iLaγA + iLbγB + iLcγC (8)

VC1 VC(2n−1) − + ... − + iγ di V − V SA1 SB1 SC1 Lk k kN Va = (9) V + La − A + dt L i La B. Converter Analyses Vb VLb N + − B V γ D1 D2 ... D(2n−1) D2n iLb This assumptions are made to the next analyses [5]

Vc V • All of the circuit elements are ideal, and there’s no power + Lc − C iLc − loss; SA2 SB2 SC2 • All capacitors are large enough therefore it’s possible to ... − + − + R ignore the ripple effect and the voltage drop; VC2 VC2n − + Vo • The converter operates under steady-state condition; Fig. 2: Matrix converter With CW voltage multiplier. • During the inductor demagnetization, only one diode will conduct; • The three-phase ac source is balanced; A. Matrix Converter Deﬁning the voltage in each capacitors (VCi) in order of the output voltage and number of stages, VCi can be expressed as Applying Power Factor Correction (PFC) techniques and ( Vo 2n , with i=1. operating under continuous conduction mode (CCM), due to VCi = (10) Vo topological restrictions, the matrix converter only have eight n , with i = 2,3,...,2n. switching states possible. For the three different arms in the Assuming unitary power factor AC voltages and AC cur- matrix converter the variable γk is deﬁned as rents can be expressed as

( 1 → Sk1 on e Sk2 off. Va = Vmsinωt γk = (6) ◦ 0 → Sk1 off e Sk2 on. Vb = Vmsin(ωt + 120 ) (11) ◦ Vc = Vmsin(ωt − 120 ) with k=A,B,C.

with the auxiliary variable γk, the eight possible states are represented in TABLE I iLA = Imsinωt ◦ iLB = Imsin(ωt + 120 ) (12) ◦ iLC = Imsin(ωt − 120 ) γA γB γC Where Vm and Im are the amplitude of the voltage and the 0 0 0 1 0 0 current respectively, and ω the angular frequency of the AC 1 1 0 source. 0 1 0 According to the polarities of the three-phase voltages, CW 0 1 1 0 0 1 converter will present different behaviors. Dividing one cycle 1 0 1 of the AC source into six sectors, as shown in Fig. 3, the 1 1 1 converter presents two different conduction Modes. Mode I for i < 0 i > 0 TABLE I: Switching states γ and Mode II for γ . Depending on the temporal location of the AC source, one of the matrix converter arm will always present γk = 1 and then γk = 0 when the conduction Mode changes. With that, there will be four different switching states for each conduction Mode. With V representing the input voltage of the CW converter γ Representing the three-phase voltages and the six sectors diLk and iγ the input current, V , iγ and are deﬁned as And the ﬁxed arms in each sector kN dt 30◦ 90◦ 150◦ 210◦ 270◦ 330◦ V  1 Vo  Vb + V c V b V a diLb 3 2n di  = Lk = dt L (15) dt 1 Vo  Vc + diLc  = 3 2n dt L

VC1 VC(2n−1) t − − + ... + iγ SA1 SB1 SC1 Va V + La − A +

iLa

Vb VLb N + − B V γ D1 D2 ... D(2n−1) D2n iLb

Vc V + Lc − C

iLc −

Fig. 3: AC source voltages. SA2 SB2 SC2 ... − + − + R VC2 VC2n − + Sector θ[◦] Brao Fixo Vo Fig. 5: Sector I Mode I State 2. I -30 ∼ 30 γA II 30 ∼ 90 γB  III 90 ∼ 150 γC 1 Vo VBN = IV 150 ∼ 210 γA V = 3 2n V 210 ∼ 270 γ kN 2 V (16) B V = − o VI 270 ∼ 330 γC  CN 3 2n

TABLE II: Sector and ﬁxed arm iγ = ic (17)

 1 Vo  Vb − diLb 3 2n di  = Lk = dt L (18) Analyzing sector I for both Modes it’s possible to determi- dt 2 Vo  Vc + diLb diLc diLc nate the slopes of and .  = 3 2n dt dt dt L Vo For Mode I, with γA = 0 and Vγ = − 2n , making use of equations (7) (8) and (9) the operation of the four circuit states VC1 VC(2n−1) − + ... − + can be detailed as iγ SA1 SB1 SC1 Va V + La − A + V VC1 C(2n−1) iLa − + ... − + iγ Vb S S S V A1 B1 C1 N + Lb − B Vγ ... V D1 D2 D(2n−1) D2n a i V Lb + La − A +

iLa Vc V + Lc − C Vb iLc − VLb N + − B V γ D1 D2 ... D(2n−1) D2n iLb SA2 SB2 SC2 ... Vc − + − + VLc R + − C VC2 VC2n iLc − − + Vo

SA2 SB2 SC2 ... Fig. 6: Sector I Mode I State 3. − + − + R VC2 VC2n − +  Vo 2 V V = − o Fig. 4: Sector I Mode I State 1.  BN 3 2n VkN = 1 V (19) V = o  CN 3 2n

 iγ = ib (20) 1 Vo VBN = − VkN = 3 2n (13)  1 Vo 2 Vo V = −  Vb +  CN diLb 3 2n 3 2n di  = Lk = dt L (21) dt 1 Vo  Vc − diLc i = i + i = −i (14)  = 3 2n γ b c a dt L VC1 VC(2n−1) VC1 VC(2n−1) − + ... − + − + ... − + iγ iγ SA1 SB1 SC1 SA1 SB1 SC1 Va Va V V + La − A + + La − A +

iLa iLa

Vb Vb VLb VLb N + − B V N + − B V γ D1 D2 ... D(2n−1) D2n γ D1 D2 ... D(2n−1) D2n iLb iLb

Vc Vc V V + Lc − C + Lc − C

iLc − iLc −

SA2 SB2 SC2 SA2 SB2 SC2 ...... − + − + − + − + R R VC2 VC2n VC2 VC2n − + − + Vo Vo Fig. 7: Sector I Mode I State 4. Fig. 9: Sector I Mode II State 2.

( VBN = 0 VkN = (22) VCN = 0  2 Vo di Vb +  Lb = 3 2n diLk  iγ = 0 (23) = dt L (30) dt 1 Vo  Vc − diLc 3 2n   = diLb Vb dt L  = diLk  dt L = di V (24) dt  Lc = c  VC1 VC(2n−1) dt L − + ... − + iγ SA1 SB1 SC1 For Mode II, with γA = 1, the polarities of the diodes Va VLa Vo + − A + change having now Vγ = 2n iLa

Vb VLb N + − B V γ D1 D2 ... D(2n−1) D2n VC1 VC(2n−1) iLb − + ... − + iγ Vc SA1 SB1 SC1 V + Lc − C Va V iLc − + La − A +

iLa SA2 SB2 SC2

Vb ... + − V − + + Lb − R N B V VC2 VC2n γ D1 D2 ... D(2n−1) D2n i Lb − + Vo

Vc V + Lc − C Fig. 10: Sector I Mode II State 3. iLc −

SA2 SB2 SC2 ...  − + − + 1 V R o VC2 VC2n VBN = − +  Vo VkN = 3 2n (31) 2 Vo Fig. 8: Sector I Mode II State 1. VCN = −  3 2n

( VBN = 0 VkN = (25) iγ = −ic (32) VCN = 0

iγ = 0 (26)  1 Vo di Vb −  Lb = 3 2n  diLk  diLb Vb = dt L (33) di  = dt 2 Vo Lk dt L  Vc + = di V (27) diLc 3 2n dt  Lc = c  =  dt L dt L   2 Vo 1 Vo  VBN = − VBN = −  3 2n VkN = 3 2n (28) VkN = (34) 1 Vo 1 Vo V = VCN = −  CN 3 2n 3 2n

iγ = −ib (29) iγ = ia (35) VC1 VC(2n−1) diLb diLc − + ... − + Sector Mode State γA γB γC iγ iγ dt dt SA1 SB1 SC1 1 1 + 1 + -iLa < 0 Va VLa 2 0 - 1 + i < 0 + − A + I 0 Lc iLa 3 1 + 0 - iLb < 0

Vb 4 0 - 0 - 0 V N + Lb − B I Vγ ... D1 D2 D(2n−1) D2n 1 1 - 1 - 0 iLb 2 0 + 1 - -iLb > 0 Vc II 1 V + Lc − C 3 1 - 0 + -iLc > 0 iLc − 4 0 + 0 + iLa > 0 di di SA2 SB2 SC2 γ γ La γ Lc ... B A C − + − + dt dt R VC2 VC2n 1 1 + 1 + 0 − + Vo 2 0 - 1 + -i < 0 I 1 La Sector I Mode II State 4. 3 1 + 0 - -iLc < 0 Fig. 11: 4 0 - 0 - i < 0 II Lb 1 1 - 1 - -iLb > 0 2 0 + 1 - i > 0 II 0 Lc 3 1 - 0 + iLa > 0  1 Vo 4 0 + 0 + 0 di Vb + diLa diLb  Lb = 3 2n γC γA γB diLk  dt dt = dt L (36) 1 1 + 1 + -iLc < 0 dt 1 Vo 2 0 - 1 + i < 0 di Vc + I 0 Lb  Lc 3 2n 3 1 + 0 - iLa < 0  = 4 0 - 0 - 0 dt L III 1 1 - 1 - 0 Completed the analyses for Sector I, the same procedure 2 0 + 1 - -i > 0 II 1 La is applied for the remaining Sectors. Through TABLE III all 3 1 - 0 + -iLb > 0 possible states describe the behavior of each one of the three- 4 0 + 0 + iLc > 0 diLb diLc γA γB γC phase currents. dt dt 1 1 + 1 + 0 2 0 - 1 + -i < 0 I 1 Lb 3 1 + 0 - -iLc < 0 4 0 - 0 - i < 0 C. Output Voltage Control IV La 1 1 - 1 - -iLa > 0 To achieve unitary power factor and the wanted voltage 2 0 + 1 - i > 0 II 0 Lc level, this work uses a closed-loop controller. Using an outer 3 1 - 0 + iLb > 0 voltage loop and since the dynamics of the output voltage is 4 0 + 0 + 0 diLa diLc γB γA γC much slower than the input current, the output voltage control dt dt is done by slowly varying the reference input current through 1 1 + 1 + -iLb < 0 2 0 - 1 + i < 0 an inner current loop [6]. Comparing the output voltage with a I 0 Lc 3 1 + 0 - iLa < 0 voltage reference, Vref , an error will be generated. Feeding the 4 0 - 0 - 0 V error into a proportional-integral compensator will generate the 1 1 - 1 - 0 2 0 + 1 - -i > 0 required amplitude for the three-phase currents. Synchronizing II 1 La 3 1 - 0 + -iLc > 0 the required amplitude signal and comparing with the three- 4 0 + 0 + iLb > 0 phase currents three errors will be generated. According to diLa diLb γC γA γB those errors and depending on the Sector and Mode signals the dt dt 1 1 + 1 + 0 switching state is chosen using TABLE III. In order to improve 2 0 - 1 + -i < 0 I 1 La the output voltage ripple, through equation (4), increasing the 3 1 + 0 - -iLb < 0 4 0 - 0 - i < 0 output matrix converter frequency, the ripple will decrease. VI Lc 1 1 - 1 - -iLc > 0 2 0 + 1 - i > 0 II 0 Lb Voref + Vo 3 1 - 0 + iLa > 0 Tzs +1 G ILk R + 4 0 + 0 + 0 Tps Tds +1 sR(C/n)+1 - Compensador TABLE III: Currents slope

Fig. 12: Block diagram of the voltage controller. Through equation (4), and switching the source frequency fs with the matrix converter output frequency fo, the capacitance can be calculated as D. Design Considerations i n(n + 1) 1) Capacitor voltage stress and capacitance: According C = o (37) V o foδVo,fo 2 to equation (10), the voltage stress across C1 is 2n and the Vo remaining capacitors n . For the determination of the capaci- 2) Boost inductor: Even the topology of the proposed tance, the output voltage ripple is used as the design criteria. converter is different from traditional boost-type rectiﬁers, the 5 switching strategies can easily adapt, so the design criteria x 10 of the boost inductors are also available for the proposed 3 converter [5]. 2

√ Vo (V) 3V t 1 L = m on,min (38) ∆iLk,max 0 0 0.5 1 1.5 Tempo (s) with ton,min the minimum turn on time of the switches and Fig. 13: Output voltage. ∆iLk,max the expected percentage of the maximum peak-to- peak ripple. 5 3) Voltage and Current stresses on switches and diodes: x 10 Assuming unitary efﬁciency, the current stress on switches and 2.1 diodes can be derived as 2 Vo (V) Po 1.9 iLkef = (39) 3Vkef 1.8 1.43 1.44 1.45 1.46 1.47 1.48 1.49 Tempo (s) with iLkef and Vkef representing the current and the voltage Zoom-in in the voltage output waveform. rms value and Po the output power. Fig. 14: The voltage stress across the switches and diodes can be calculated by equation (40) and (41) respectively 2000 1000 Vo,max VImax = (40) 0 2n Va (V) −1000

Vo,max −2000 V = (41) 1.3 1.35 1.4 1.45 1.5 Dmax n Tempo (s) E. Simulations (a) Phase A voltage

Through the MATLAB/Simulink software, a simulation is 5000 made of the matrix converter and the CW voltage multiplier proposed topology. Aiming to convert 690V phase-phase volt- 0 age generated by a wind turbine to 200kV DC voltage, due iLa (A) to computational limitations, the Cockcroft-Walton will have −5000 a limit of 50 stages. The system speciﬁcation for the proposed 1.3 1.35 1.4 1.45 1.5 converter is summarized as follows: Tempo (s) (b) Phase A current

Parameters Value Units Fig. 15: Voltage and current in fase A. Vo 200, 000 V fo 4, 000 Hz R 20, 000 Ω P o 2, 000, 000 W IV. CONCLUSIONS n 50 Lk 0.181 mH In this study, a three-phase AC-DC boost converter based on Ci 50.731 µF Cockcroft-Walton was designed to convert 690V AC phase-to- TABLE IV: Circuit parameters phase to 200 kV DC. Using a matrix converter it was possible to convert a three-phase voltage into a single-phase and to control the matrix converter output frequency, reducing the output ripple to 5% of the mean output voltage value. The Analyzing Fig. 13, there is an initial discharge in the matrix converter input current shows a sinusoidal wave and a capacitors, because it starts with an initial voltage close to the nearly unitary power factor validating the control techniques final one, occurring subsequently the transitory until it reaches used. With a Cockcroft-Walton converter with 50 stages it was the 200kV voltage. Zooming-in the steady state of the output possible to achieve the desired output voltage of 200 kV voltage in Fig. 14, it is possible to observe an output voltage ripple of about 10kV, representing 5% of the mean output REFERENCES value. [1] Rui MG Castro. Energias renovaveis´ e produçao˜ descentralizada– Observing Fig. 15, the unitary power factor is achieved, introduçao˜ a` energia eolica.´ Lisboa, Universidade Tecnica´ de validating the PFC techniques used. Lisboa, 86p, 2007. [2] Melvin M Weiner. Analysis of cockcroft-walton voltage multi- pliers with an arbitrary number of stages. Review of Scientific Instruments, 40(2):330–333, 1969. [3] Ioannis C Kobougias and Emmanuel C Tatakis. Optimal design of a half-wave cockcroft–walton voltage multiplier with minimum total capacitance. Power Electronics, IEEE Transactions on, 25(9):2460–2468, 2010. [4] JS Brugler. Theoretical performance of voltage multiplier circuits. Solid-State Circuits, IEEE Journal of, 6(3):132–135, 1971. [5] Chung-Ming Young, Hong-Lin Chen, and Ming-Hui Chen. A cockcroft–walton voltage multiplier fed by a three-phase-to- single-phase matrix converter with pfc. IEEE Transactions on Industry Applications, 50(3):1994–2004, 2014. [6] Jose´ Fernando Alves Silva. Electronica´ industrial– semicondutores e conversores de potencia.ˆ Fundaçao˜ Calouste Gulbenkian, 2a ediçao˜ , 2013.